© IEOM Society

Improving the quality of engineering education: using a Pitot tube

system at fluid mechanics laboratories

Pedro José Gabriel Ferreira, Iara Batista de Lima, Túlio Cearamicoli Vivaldini, Alexandre

Daliberto Frugoli, Pedro Américo Frugoli

ICET – Instituto de Ciências Exatas e Tecnologia

Universidade Paulista – UNIP

Rua Dr. Bacelar, 1212, ZIP CODE: 04026-002, São Paulo-SP, Brazil

pedrojfg@unip.br , iblima@unip.br , tuliocv@unip.br

alefrugoli@unip.br , pedrofrugoli@unip.br

Thaís Cavalheri dos Santos

ICET – Instituto de Ciências Exatas e Tecnologia

Universidade Paulista – UNIP

Rua Dr. Bacelar, 1212, ZIP CODE: 04026-002, São Paulo-SP, Brazil

FTCE – Faculdade de Tecnologia e Ciências Exatas

Universidade São Judas Tadeu – USJT

Rua Taquari, 546, ZIP CODE: 03166-000, São Paulo-SP, Brazil

thais_cavalheri@yahoo.com.br

Abstract In the present work, academic results concerning modifications in fluid mechanical laboratories and measurements

with a simple Pitot tube at a Brazilian university are presented. Considering the current objectives of engineering

teaching, the Physics Education Research Group (GruPEFE) has been developing didactic materials and

technologies at fluid mechanics laboratories, which are used by approximately ten thousand students in several

engineering fields, per semester. The group has a research field dedicated to develop cheaper and faster technologies

for practical class optimization, which leads to a higher-level learning, as it creates an analyzing environment and

promote an active learning at the laboratories. In this context, results concerning a simple Pitot experiment are

presented with some important issues that can be addressed in practical classes as the relationship between velocity

and flow rate and the water velocity profile in a fully developed pipe flow. A good agreement (± 2%) between the

theoretical and the experimental fluid velocity profile was found.

Keywords

Fluid mechanics, engineering education, Pitot tube, water velocity profile.

1. Introduction During the last years, universities rationalized their engineering curricula, associated with cost cuts that have led to a

reduction of credit hours, as point out by Russel et al. (2000). According to Agrawal and Khan (2008) education

quality is a matter of concern for all its stakeholders, which requires educators and educational administrators to

demonstrate that educational institutions are capable of providing high-quality educational opportunities at a

reasonable cost.

In this context, the Physics Education Research Group (GruPEFE) was created at engineering undergraduate course

at Universidade Paulista (UNIP), located in Brazil, which teaches engineering since 1977. In order to get results in

agreement to the engineer professional life, the group has a research field dedicated to develop cheaper and faster

technologies for practical class optimization. Considering the current objectives of engineering teaching, the

GruPEFE is developing didactic materials (Ferreira and Cavalheri (2014) and Santos and Ferreira (2015)) and

technologies at fluid mechanics laboratories, which are used by approximately ten thousand students in several

engineering fields (Civil, Mechanical, Automation, Production, Aeronautical and Petroleum), per semester.

Proceedings of the 2015 International Conference on Operations Excellence and Service Engineering

Orlando, Florida, USA, September 10-11, 2015

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The teacher and student experiences in classroom are considered to develop new didactic equipment and

methodologies, as a new Pitot tube system, which will be described in the present work. Pitot tube systems are

widely used by industry and research. In literature, Replogle and Wahlin (2000) present a simple Pitot tube system

developed with cheaper materials and that can be used to measure the fluid velocity at several points across the piper

diameter (in a system to lift water in canals). Lynn et al (2014) describe an S-type Pitot tube system to determine

fluid velocity at low flows (< 2.4 m³/h) and pressure difference (< 100 Pa).

Based on the above, the GruPEFE has performed some improvements on fluid mechanics laboratories and

developed an economical, practical and robust Pitot tube system able to measure low-pressure difference ( 50 Pa)

in a 32 mm cross section of a pipe, analyzing different flow values (from 7.25 to 8.5 m³/h). This system provides

experimental results consistent with fluid mechanicals theory. The main purpose of the system improvements

summarized above was to optimize practical classes and lead to higher-level learning, as it creates an analyzing

environment, promote an active learning at the laboratories and enhance the student interest on the physical

phenomena associated (Matthews (2000)). This new approach is based on the education philosophy of

constructivism formulated by John Dewey (1938) and on the education philosophy of critical pedagogy, which was

influenced and widespread in Brazil by Paulo Freire (2000). From these perspectives the main focus should be on

activities inside classroom, on which instruction must create an active role for the learner and the learner must

construct his own knowledge by the means of a critical reflection of the concepts presented in class.

2. Materials and Methods The setup developed for practical classes of fluid mechanics consists of a stainless steel pipeline (see Figure 1-a)

with different branches, allowing multi parametrical measurements. Previously, all the pipes were made of PVC.

Although, PVC is a cheap material its durability and maintenance are not suitable, considering the extensive usage

of the fluids workbench at the fluids laboratories in UNIP. Moreover, PVC is strongly influenced by temperature

variation which caused leak problems during the practical classes.

(a) (b)

Figure 1: (a) System used for fluid mechanics practical classes and (b) rotameters connected to the water pumps.

The fluid analyzed is water and this system allows studying different fluid meters (Pitot tube, Venturi and orifice

meter), valve flow characteristics, singular and distributed head losses and pump association (series or parallel)

(Figure 2). Furthermore, the system has rotameters (0.5 m³/h resolution) connected to the pumps, which enables

measuring the flow rate of water (Figure 1-b). In one of the pipe branches, there is an acrylic tube (40 mm diameter)

inserted with a simple Pitot tube, made of stainless steel, in which the distance can be varied across the acrylic tube

by the means of a linear scale (1.0 mm resolution). Details of this assembly are depicted in Figure 3.

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Figure 2: View of the system, showing the valves and pipes used to study singular head losses: (a) Globe (b) ball

and (c) gate valve; (d) curved and (e) elbow pipe. Flow meter connected to the system: (f) Venturi tube.

(a) (b)

Figure 3: (a) Schematic drawing of Pitot tube with linear scale to study the fluid velocity profile across the tube

diameter (b) View of the Pitot tube in the system.

Previously, u-tube manometers filled with mercury were used at the fluid mechanics laboratories for pressure drop

measurements across the Pitot tube. With the u-tube manometers the students had to relate the differential pressure

ΔP with the observing difference h between the levels of mercury in the two halves of the u-tube, using the

differential manometer equation ΔP= (γHg- γwater).h, where γHg is the specific weight of mercury and γwater is the

specific weight of water. Therefore, to perform differential pressure measurements with u-tube manometer near to

the wall of the pipes, which is the objective of the Pitot experiment, was a difficult task since it resulted in values of

the same magnitude as the instrumental resolution. Then, in order to increase the system sensitivity to low

differential pressure, the mercury was replaced by bromoform as manometer fluid, but since bromoform is toxic, to

reduce the occupational exposure to this fluid and provide the required sensitivity, minimizing the data acquisition

time, digital manometers were specially developed for that purpose (see Figure 4).

(a) (b) (c)

(f) (e) (d)

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Figure 4: Digital manometer specially developed for fluid mechanics practical classes.

From fluid mechanics theory (Fox and McDonald’s (2011) and Brunetti (2008)), the fluid velocity v1 can be

determined considering the Bernoulli equation at point (1) and (2) on a streamline (Figure 2-a):

22

water

22

21

water

11 v

g2

1pzv

g2

1pz

(1)

where:

v1 and v2 are the fluid flow velocity at points (1) and (2) on a streamline;

g is the value of acceleration due to gravity;

z1 and z2 are the elevation of the points above a reference plane;

p1 and p2 are the pressure at the chosen points, and

γwater is the specific weight of the water at all points in the fluid and the value considered in the following analyses

was 10000 N/m³.

Thus, as the velocity at the stagnation point of Pitot tube is zero, the fluid velocity v1 can be calculated by the

following relation:

water

121

)pp(g2v

(2)

Therefore, by connecting a manometer to the Pitot tube and at the pipe wall is possible to measure the pressure drop

across points (1) and (2), and so determine de fluid velocity. In the present work, results concerning a simple Pitot

experiment are presented with some important issues that can be addressed in practical classes as the relationship of

velocity and the flow rate (ranging from 7.25 to 8.5 m³/h) and the agreement between the theoretical and the

experimental water velocity profile in a fully developed pipe flow, considering that the velocity profile v can be

written in terms of the maximum velocity (vmax) as:

2

maxR

r1vv (3)

where r is the position from the pipe center and R is the pipe radius.

Furthermore, the standard system has two pumps with similar performances (550 W), so the influence of the pump

association (in series or parallel) can be analyzed.

3. Results and Discussion In order to test the reliability of the instruments and to validate the didactic technique, measurements of differential

pressure across 32 mm of the pipe, with three different manometers and a volumetric flow rate equal to 8.7 m³/h

were performed using two pumps in series. By means of Equation (2), the water velocity was determined and the

results are shown in Figure 5-a. It is worth noting that the error bars represented consist with instrumental

uncertainties and correspond to ± 10% of the velocity value. The discrepancies of data sets are due to the calibration

of the manometers, but since the main objective of this practical class is to study the Pitot tube operating principle

and not to perform absolute precise measurements, these variations are irrelevant.

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In Figure 5-b the velocity data determined from the differential pressure, measured by the three manometers were

normalized to the maximum value. Therefore, is possible to verify the consistency of the result trends from the

different manometers developed for the fluid laboratories. Considering this simple experiment and analysis is

possible to discuss concepts taught in classroom in former semesters of the engineering courses as differential

pressure measurements and meters, the Pitot tube principle of operation and fully developed flow among infinite

parallel plates. According to the basic fluid mechanics theory (Fox and McDonald’s (2011) and Brunetti (2008)),

this parabolic profile is due to the fact that close to the pipe walls the friction causes a decrease in fluid velocity. On

the other hand, for incompressible flow, mass conservation requires that the velocity in the central frictionless region

of the pipe must increase to compensate.

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5

-20

-15

-10

-5

0

5

10

15

20

Manometer_1

Manometer_2

Manometer_3

Po

sit

ion

(m

m)

Velocity (m/s)

Pumps in Series

0.0 0.2 0.4 0.6 0.8 1.0 1.2

-20

-15

-10

-5

0

5

10

15

20

Manometer_1

Manometer_2

Manometer_3

Po

sit

ion

(m

m)

Normalized Velocity

Pumps in Series - Normalized Velocity

(a) (b)

Figure 5: (a) Water velocity profile in a 40 mm diameter pipe measured with a Pitot tube with three different

manometers developed for practical classes with volumetric flow rate equal to 8.7 m³/h and (b) Normalized velocity

across the pipe considering the differential pressure measured by the three manometers analyzed.

The agreement between water velocity values across the pipe obtained in three independent data sets named Data1,

2 and 3, measured with the manometer_2 and with two water pumps in series are shown in Figure 6 and evidence

the repeatability of the results and the system stability.

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0

-20

-15

-10

-5

0

5

10

15

20

Pumps in series

Data 1

Data 2

Data 3

Po

sit

ion

(m

m)

Velocity (m/s)

Figure 6: Data sets referring to independent measurements performed with manometer_2 and two water pumps in

series.

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The parabolic shape of the velocity profile was analyzed by means of fitting the function shown in Equation (3) to

“Data 2” (Figure 7). It is worth noting that, for didactic purposes the water velocity is analyzed in the horizontal axis

and the radial position in a pipe in the vertical axis, but in Figure 5 the position, which is the independent variable, is

kept in the horizontal axis. The agreement (± 2%) between the experimental data and the theoretical curve is evident

in Figure 5.

-20 -15 -10 -5 0 5 10 15

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

Data 2

Parabola Fit

Ve

loc

ity

(m

/s)

Position (mm)

Figure 7: Parabolic fit of experimental Data 2, considering the theoretical velocity profile in a fully developed pipe

flow.

As previously mentioned, with the present system the influence of the water pump association can be studied. When

the pumps are in series their flow rates are identical and the heads produced are added. Whereas when pumps are in

parallel the generated head is the same for the pumps and the total flow rate is the sum of the flow rates of each

pump. Thus, in order to study this influence, measurements of the velocity profile across the pipe were performed

with both associations and are presented in Figure 8. In this analysis, both measurements agree within their quoted

uncertainties.

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5

-20

-15

-10

-5

0

5

10

15

20

Pumps in series

Pumps in parallel

Po

sit

ion

(m

m)

Velocity (m/s)

Figure 8: Water velocity across a pipe, measured with a Pitot tube and using two pumps in series and two pumps in

parallel.

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In order to study the qualitatively relation between the fluid velocity and the flow rate, measurements of the

maximum velocity (at the central axis of the pipe) were performed with the Pitot tube, connecting the two pumps in

series and in parallel (see Figure 9). As expected, no significant difference was observed.

7.0 7.5 8.0 8.5

1.5

2.0

2.5

3.0

3.5

Pumps in series

Pumps in parallel

Ve

loc

ity

(m

/s)

Flow rate (m³/h)

Figure 9: Fluid velocity versus flow rate data with pumps connected in series and in parallel.

Conclusions Based on the current objectives of the engineering teaching, the GruPEFE is developing didactic materials and

technologies at fluid mechanics laboratories. In this context, our group has developed an economical, practical and

robust Pitot tube system able to measure low-pressure difference across a pipe and analyze different fluid flow rates.

This system provides experimental results concerning water velocity profile in good agreement with fluid

mechanicals theory, which is demonstrated by the use of the parabolic fit of a fully developed flow.

The improvements performed in systems optimized practical class and create an analyzing environment, promoting

an active learning at the laboratories and enhancing the student interest on the physical phenomena associated.

Furthermore, since Pitot tubes are widely used by industry and research area, this measuring system provides results

in agreement to the engineer professional life.

References Agrawal, D. K., and Khan, Q. M., A quantitative assessment of classroom teaching and learning in engineering

education, European Journal of Engineering Education, vol. 33, no. 1, pp. 85-103, 2008.

Baldock, T. E., and Chanson, Undergraduate teaching of ideal and real fluid flows: the value of real-world

experimental projects, European Journal of Engineering Education, vol. 31, no. 6, pp. 729-739, 2006.

Brunetti, F. Mecânica dos Fluidos, Pearson Prentice Hall, São Paulo, 2008.

Dewey, J., Experience and education. New York: Collier Books, 1938.

Ferreira, P. J. G.; Cavalheri, T. Estática dos Fluidos. São Paulo. ISBN: 978-85-917144-0-7, 2nd Ed., São Paulo,

2014.

Freire, P., Pedagogy of the Oppressed, 30th Anniversary ed. New York: Continuum, 2000.

Fox, R., W., and Mcdonald’s, A. T., Introduction to Fluid Mechanic, 8th edition, John Wiley & Sons, United States

of America, 2011.

Lynn, R. J., Haljasmaa, I.V., Shaffer, F., Warzinski, R.P., Levine, J.S., A Pitot tube system for obtaining water

velocity profiles with millimeter resolution in devices with limited optical access, Flow Measurement and

Instrumentation, vol. 40, pp. 50-57, 2014.

Mathews, M., Construtivismo e o Ensino de Ciências: Uma Avaliação, Cad. Cat. Ens. Fís., v. 17, n. 3: pp. 270-294,

dez. 2000.

Replogle, J., and Wahlyn, B., Pitot-Static Tube System to Measure Discharges From Wells, Journal of Hydraulic

Engineering, vol. 126, no. 5, pp. 335-346, 2000.

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Russell, J.S., Stouffer, B. and Walsh, S.G., The first professional degree: a historic perspective. J. Profess. Issues

Engng Educ. Pract., ASCE, 2000, 126, 54–63.

Santos, T. C. and Ferreira, P. J. G. Fenômenos de Transporte. ISBN: 978-85-917144-1-4, 1st Ed., São Paulo, 2014.

Biography Pedro José Gabriel Ferreira is currently coordinator of Engineering Course, professor, coordinator of laboratories

and member of GruPEFFE at Universidade Paulista – UNIP. Mr Ferreira holds Bachelor a degree in Control and

Automation Engineering from Universidade Paulista – UNIP, concluded in 2004. After graduating, he studied from

2006 to 2007 a post-graduation course (latu sensu) in Teacher Training for Higher Education at UNIP. In 2009 he

enrolled in a post-graduation Masters in Production Engineering from UNIP and concluded it in 2011. From 2004 to

2009 worked as an Engineer at Ultragaz Company in the liquefied petroleum gas market. The main activities

developed were in the areas of Production, Maintenance, Engineering Projects, Industrial Painting Process,

Inspection of pressure vessels and technical tests.

Iara Batista de Lima is currently professor of Engineering Course (Fluid Mechanics and Physics disciplines) and

member of GruPEFE at Universidade Paulista - UNIP. Ms. Lima holds a Bachelor degree in Physics (2008) from

Pontifícia Universidade Católica de São Paulo – PUC, a Master of Science degree (2010) and a PhD degree in

Science (2014) – nuclear technology – applications - from Universidade de São Paulo (USP), which is a Nuclear

Technology Program of the Instituto de Pesquisas Energéticas e Nucleares (IPEN). Her research interests include

experimental methods and instrumentation for elementary particles and nuclear physics and practical activities

applied to Engineering Course.

Túlio Cearamicoli Vivaldini is currently professor of Engineering Course (Physics disciplines: laboratory and

theory) and member of GruPEFE at Universidade Paulista - UNIP. Mr. Vivaldini holds a Bachelor degree in Physics

(2008) from Pontifícia Universidade Católica de São Paulo – PUC, a Master of Science degree (2010) and a PhD

degree in Science (2014) – nuclear technology – applications - from Universidade de São Paulo (USP), which is a

Nuclear Technology Program of the Instituto de Pesquisas Energéticas e Nucleares (IPEN). His research interests

include experimental methods and instrumentation for elementary particles and nuclear physics and practical

activities applied to Engineering Course.

Alexandre Daliberto Frugoli is currently Vice Dean Advisor of Planning, Administration and Finance and of

Institute of Exact Sciences and Technology - ICET, coordinator of Engineering Course, professor (Physics and

Fluids) and member of GruPEFFE at Universidade Paulista – UNIP. Mr Frugoli holds a Bachelor degree in

Mechanical Engineering from Universidade Paulista – UNIP, completed in 1996. In 1997 he enrolled in a post-

graduation in Production Engineering by UNIP and got Master of Science degree in 2000. In 2013 got a PhD degree

in Production Engineering from UNIP.

Pedro Américo Frugoli is currently Director of the Institute of Exact Sciences and Technology - ICET, coordinator

of Engineering Course, professor of Physics, and member of GruPEFE at Universidade Paulista – UNIP. Mr Frugoli

holds a Bachelor degree in Physics from Universidade de São Paulo (USP), completed in 1973. In 1974 Mr. Fugoli

enrolled in a Physics post-graduation program at USP, concluded in 1981. In 2012 he got a PhD degree in

Production Engineering from UNIP.

Thais Cavalheri dos Santos is currently coordinator of technical course in buildings (PRONATEC), professor of

Engineering Course at Universidade Paulista – UNIP and professor of Engineering Course at São Judas Tadeu

University. Mrs. Cavalheri holds a Bachelor degree in Medical Physics from Universidade de São Paulo – USP,

completed in 2005. After graduating, she enrolled in a Masters in Science (Physics) Program of Physics applied to

Medicine and Biology in USP, concluded in 2007. Simultaneously with the Masters course she studied a post-

graduation course (latu sensu) in Business Administration – MBA in Management of Hospitals and Health Systems

by Fundação Getúlio Vargas. In 2012 she got a PhD degree in Science – nuclear technology – applications - from

Universidade de São Paulo (USP), which is a Nuclear Technology Program of the Instituto de Pesquisas Energéticas

e Nucleares (IPEN). After completing PhD she remained as a researcher at IPEN until 2014, when she got her post-

PhD.

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